Firing point locator system



Nov. 6, 1962 F. G.

STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet l Nov. 6,1962 F. G. STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 23, 1957 6 Sheets-Sheet 2 E 2;/aff/7% l Nov. 6, 1962 F, G. STEELE 3,063,047

FIRING POINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet 3 4,00//402 fJ/Y/a/ar l n l 40/ 412, l /4f4 Nov. 6, 1962 F. G. STEELE FIRINGPOINT LOCATOR SYSTEM Filed Jan. 25, 1957 6 Sheets-Sheet 4 Wwe u Norac'zaczw/.f 2074/704/ Nov. 6, 1962 F. G. STEELE FIRING POINT LOCATORSYSTEM Filed Jan. 25, 195'? 6 Sheets-Sheet 5 6 Sheets-Sheet 6 F. G.STEELE FIRING POINT LOCATOR SYSTEM Nov. 6, 1962 Filed Jan. 23, 1957United rates Patent @nace il a 3,063,647 FIRING POINT LCATOR SYSTEMFloyd G. Steele, La Jolla, Calif., assigner to Digital Control Systems,Inc., La Jona, Calif. Filed Jan. 23, 1957, Ser. No. 635,9l6 28 Claims.(Cl. 343-7) This invention relates to a ring point locator system fordetermining the tiring point of a projectile, and more particularly to atiring point locator system which utilizes a digital computer fordetermining the position and veloc` ity of a projectile at a point onits trajectory, and which is thereafter operable -to iterativelyextrapolate the trajectory equations of the projectile to determine thefiring point thereof.

`It has long been recognized that the effectiveness of artillery andmortar re would be sharply reduced if there was some manner toaccurately and rapidly locate the tiring point of the projectiles tiredthereby. Following the development of accurate tracking radars which arecapable of tracking a projectile through at least a portion of itstrajectory, various attempts have been made to construct firing pointlocators by utilizing the data produced -by ythe radar during itstracking mode to simulate the earlier portion of the trajectory andthereby indicate the projectiles firing point.

One of the first firing point locator systems suggested in the prior artincluded a plotting board which was utilized to plot the trajectory of aprojectile while it was being tracked, after which the operator manuallyextrapolated the curve backward to indicate lthe projectiles ring point.The principal disadvantage of this system is that it is subject to humanerror and produces results which are grossly inaccurate when comparedwith the degree of accuracy necessary to reasonably insure subsequentdestruction of the enemy weapon by friendly lire.

In still other prior art firing point locator systems analog computingelements have been utilized which are responsive to the intelligencedata produced by the radar for predicting the location of the firingpoint by extrapolating simplified equations which roughly dene theballistics of the projectile. One example of this type of prior artsystem is disclosed in U.S. Patent 2,761,129, issued August 28, 1956, toE. G. Hills for Apparatus for Locating a Missile Projecting Device,wherein a trigonometric solution of a missiles trajectory in a polarcoordinate system is utilized to present the approximate tiring pointlocation on an associated plotting board, the solution of the trajectoryequations being accomplished through the addition of analog signalsrepresentative of position and the time rate of change of position.

Although analog systems which operate in the foregoing or similar mannerhave been constructed and tested, their utility is inherently restrictedby several important factors. Firstly, the accuracy provided lby thesesystems is frequently inferior to that provided by the manual plottingmethod described previously owing to the fact that the error contributedby each analog element in the system, when compounded with the errorscontributed by the other elements, produces an intolerable system error.In addition, the systems are extremely complex, bulky and expensive, andgreat care must be exercised in adjusting the various analog elements toprovide even a slight degree of accuracy and reliability.

The present invention, on the other hand, overcomes the above and otherdisadvantages of the prior art ring point locator systems by providing asystem in which a digital computer is utilized to determine first theposition and velocity of a projectile at a point on its trajectory, andwhich is thereafter operable to iteratively extrapolate the trajectoryequations of the projectile to determine the tiring point thereof. Inaccordance with the basic con- 3,063,47 Patented Nov. 6, i962 cept ofthe present invention, the tiring point locator system herein disclosedcomprises a radar operable to track a projectile through at least aportion of its trajectory to produce output signals representative ofthe instantaneous coordinate position of the projectile along each ofthe coordinates of a three dimensional coordinate system in space, ananalog-to-digital converter for converting the radar output signals toelectrical signals digitally representative of the position and timerate of change of position of the projectile at substantially themidpoint of a sampled portion of the projectiles trajectory, and anelectronic digital computer operative to extrapolate the trajectoryequations of the projectile utilizing as initial conditions the knownposition and Velocity of the projectile at a point on its trajectory.

More specifically, in the preferred embodiment of the invention hereindisclosed the analog-to-digital converter functions to generate threedifunction signal trains corresponding to the X, Y and H coordinates ofan orthogonal coordinate system and representative of the instantaneousposition of the projectile as it is being tracked, each train includinga predetermined number of sequential difunction signals. These signalsare then applied to associated binary accumulators which function todetermine the average coordinate position of the projectile during theinterval through which the signals are generated, and which alsofunction to determine the coordinate velocities of the projectile bydilferencing the average positions of the projectile during the lirstand second halves of the interval.

In order to most clearly comprehend the invention it should be herepointed out that the term difunction signal train refers to a train ofsignals each having a fixed period and having either a high levelrepresenting a irst quantity or a low level representing a secondquantity, the average values of the quantities represented by thesignals occurring over a given interval corresponding to the averagevalue of the physical quantity represented by the train during the giveninterval. For example, if it is assumed that the first and secondquantities represented by the -signals in a train are the maximum rangeof the system along the corresponding coordinate axis expressedpositively and negatively, respectively, then the average value of thesignals occurring over a given interval represents the averagecoordinate position of the projectile during the interval. the averageposition of the projectile along each coordinate may be determined byactuating an associated binary accumulator to increase its count in onedirection in response to each high level signal in the train and in theopposite direction in response to each low level signal, the binarynumber stored in the accumulator at the end of the operationcorresponding to the coordinate position of the projectile at themidpoint of the sampled portion ofv ing the signals in one group andsequentially applying the inverted signals and the remaining uninvertedsignals to an associated accumulator. The resultant binary number in theaccomulator is then representative of the difference between the averageposition of the projectile during the rst half of the sampled portion ofits trajectory and the average position during the second half of thesampled portion of its trajectory, or in other Words, the time rate ofchange of the projectiles position at the midpoint of the sampledportion of the trajectory. Y

In accordance with the invention the coordinate positions and velocitiesderived in the foregoing manner are entered as the initial conditions ina plurality of digital integrators which are interconnected toselectively extrap- In accordance with the invention, therefore, i

olate the trajectory equations for the projectile, either forward orbackward in time, to produce output signals representative of thechanges in the projectiles coordinate positions as the extrapolationprocess is carried out. These signals are then combined with the initialposition signals which are in turn utilized to actuate three digitalservos which are operative to drive three respectively associatedmechanical counters to present a visual indication of the coordinates ofthe point of the projectiles trajectory to which the trajectoryequations have been extrapolated.

Among the novel features of the present invention there is alsodisclosed a bidirection digital position servo operable to drive apositionable element to a position corresponding to the coordinateposition of a point on a projectiles trajectory in a three dimensionalcoordinate system in space. Still another novel feature of the inventionherein disclosed is the utilization in the associated digital servos ofa bidirectional quantizer which senses incremental rotational changes inthe position of a shaft by sensing changes in the inductive reactancespresented by a pair of ferromagnetic core inductors positioned adjacentthe periphery of a toothed ferromagnetic disk which rotates inaccordance with shaft rotation. A further novel feature of the quantizeris the detection of incremental changes in the shaft position bygenerating tirst and second bilevel signal trains one of which leads theother by 90 when the shaft is rotated at a fixed rate in one directionand which lags the other by 90 when the shaft is rotated at a fixed ratein the opposite direction, a change in the level of the first trainsignifying an incremental change in rotational position while thepolarity of the change is indicated by the level of the second trainwhen the first train is changing levels.

It is, therefore, an object of the invention to provide a tiring pointlocator system which functions to determine first the position andvelocity of a projectile at a point on its trajectory and which isthereafter operable to interatively extrapolate the trajectory equationsof the projectile to determine the firing point thereof.

Another object of the invention is to provide a tiring point locatorsystem which utilizes a digital computer to incrementally extrapolatethe trajectory equations of a projectile either forward or backward intime to either` verify the projectiles impact point or ascertain itstiring point.

A further object of the invention is to provide a tiring point locatorsystem which utilizes a plurality of digital integrators interconnectedin accordance with the trajectory equations of a projectile toextrapolate the trajectory backward in time to determine the projectilestiring point, the digital integrators utilizing as initial conditionsthe known coordinate positions of the midpoint of a sampled portion ofthe projectiles trajectory.

Still another object of theinvention is to provide a system fordigitally determiningthe coordinates of the midpoint of a sampledportion of the trajectory of a projectile moving in a three dimensionalYcoordinate system.

Anadditional object of the invention is to provide a system fordetermining-the coordinates of the midpoint of aV sampled portion of thepath traveled by an object'moving in space by generating a plurality ofdifunction signal trains representative of the instantaneous positionVof the object along a correspondingv plurality of coordinates in arectangular coordinate system, and accumulating the individualdifunction signals in the trains tovproduce electricalA signalsrepresentativey ofl the average coordinatev positions of the objectduring the interval it was traversing the sampled portion of its path'inspace.

It is another object Vof the invention to provide a system for digitallydetermining the coordinate velocities of a projectile moving in anorthogonal coordinate system in space at the midpoint ofv a sampledportion of the projectiles trajectory.

It is also an object of the invention to provide a system fordetermining the velocity of an object moving in an orthogonal coordinatesystem in space at the midpoint of a sampled portion of the objectstrajectory by generating a plurality of difunction signal trains eachincluding N signals and representative of the instantaneous position ofthe object along a corresponding plurality of coordinates which dene thecoordinate system, and accumulating the signals in each train to presentsignals representative of the numerical difference between the summationof the iirst N/ 2 signals in each train and the summation of the lastN/Z signals in each train.

Still a further object of the invention is to provide an inputconversion apparatus for rotating a shaft to a position corresponding tothe average value of an applied analog signal over a predeterminedperiod by generating a difunction signal train including N difunctionsignals during the period, each signal having either a first valuerepresenting a predetermined maximum value of the analog signal or asecond value representing a predetermined minimum value of the analogsignal, the average value of the N signals being proportional to theanalog signal over the period, and rotating the shaft through anincremental rotational angle proportional to the maximum or minimumvalue over N in response to each rst or second valued difunction signal,respectively.

Another object of the invention is to provide a bidirectional digitalposition servo operable to drive a positionable element to a positioncorresponding to the coordinate position of a point on a projectilestrajectory in a three dimensional coordinate system in space.

A further object of the invention is to provide a bidirectional digitalquantizer which senses incremental rotational changes in the position ofa shaft by sensing changes in the inductive reactances presented by apair of ferromagnetic core inductors positioned adjacent the peripheryof a toothed ferromagnetic disk which rotates in accordance with shaftrotation.

Still another object of the invention is to provide a bidirectionaldigital quantizer for detecting incremental changes in the rotationalposition of a shaft by producing first and second bilevel signal trainsone of which leads the other by when the shaft is rotated at a fixedrate in one -direction and which lags the other by 90 when the shaft isrotated at a tixed rate in the opposite direction, a change in the levelof the tirst train signifying an incrementaly rotational change, whilethe level of the second train at the same instant signifies the sense ofthe change.

The novel features which are believed to be characteristic of theinvention, both as to its organization and method of operation, togetherwith further -objects and `advantages thereof, will be better understoodfrom the following description considered in connection with theaccompanying drawings in which several embodiments of the invention areillustrated by way of example. It is to be expressly understood,however, that the-drawings are for the purpose of illustration anddescription only, and are not intended as a deinition of the limits ofthe invention.

FIG. l is a block `diagram of a tiring point locator system, inaccordance with the invention;

FIG. 2 is a graph illustratingthe manner in which the firing pointlocator system yof the invention determines the-coordinates andcoordinate velocities of a projectile at a point in the projectilestrajectory;

FG. 3 is a block diagram, partly in schematic form, of a digitalprojectilev tracking computer, in accordance with the invention, whichhas been employedin the system of FlG. l;

FIG. 4 is a schematic diagram of a quantizer, in accordance with theinvention, which may be utilized in the digital servos in the computerof FIG 3;

`lEGS. 5a and 5b are waveforms of signals appearing at various points inthe circuit of FIG. 4;

FGS. 6a and 6b are waveforms of the output signals produced by thecircuit of FIG. 4 illustrating the manner in which the quantizers of theinvention convey output intelligence;

FIG. 7 is a 'detailed block diagram, partly in schematic form,illustrating the principal physical components of the computer shown inFIG. 3;

FIG. 8 is a word diagram illustrating the manner in which intelligenceis stored and processed in the computer of FIG. 7; and

FIG. 9 is a schematic diagram illustrating the manner in which thelogical gating circuits lare mechanized within the computer of FIG. 7 toperform logical and arithmetic functions.

Referring now to the drawings, wherein like or corresponding parts arenow designated Iby the same reference characters throughout the severalviews, there is shown in FIG. 1 a ring point locator system, inaccordance with the invention, which includes a projectile trackingcomputer 10 operative in conjunction with a tracking radar 12 and aplurality of signal converters 14 Ifor determining either the liringpoint FP or impact point IP of a projectile shown at A2. Beforedescribing the manner in which the projectile tracking computer of theinvention performs its computational function, consideration will begiven first to the coordinates in which the system is operative and themanner in which tracking of the projectile is accomplished.

More specifically, in setting up the system shown in FIG. 1, trackingradar 12 is placed at a rselected point on the topography and thereafterserves as the origin of an orthogonal coordinate system x, y, h in whichthe computer operates, the computed coordinates of the projectilestiring point or impact being displayed by the computer in a plurality ofregisters X, Y and H. As will be described in more detail hereinafter,by merely presetting registers, X, Y and H to numbers representing themap coordinates of the tracking radar location, the ydisplay in theoutput registers after a projectile tracking operation may be utilizedto present the actual map coordinates of the tiring point or impactpoint.

In the operation of the system, radar 12 is normally operative in ascanning mode during which time the radar is utilized to scan forprojectiles which have been fired. When a projectile is detected, theoperation of the radar is changed, either manually or automatically, toa tracking -mode in which the radar locks on and tracks the projectilethrough at least a portion of its trajectory; at the start of thetracking mode the radar also transmits directly to the computer anelectrical start signal FR indicating that the computer should initiatea routine termed Fit, which will be described in detail hereinafter.

In addition to the aforementioned start signal, the radar also makesavailable to converter 14 three analog signals EX, EY and EH whosevoltages are respectively representative of the instantaneous positionof the projectile being tracked in the coordinate system x, y, h. Itwill be recognized, of course, that in a conventional radar the targetposition is presented basically in terms of range, elevation angle andazimuth angle. However, since there are numerous techniques availablefor resolving this information into an orthogonal coordinate system,further description of the structure of radar 10 is consideredunnecessary. v

As yset forth hereinbefore, the projectile tracking computer of theinvention is basically a digital device which receives its inputintelligence information in the form of bilevel signal trains whichrepresent the input intelligence digitally. Although the computer of theinvention may be readily adapted for operation upon a number ofdifferent forms of digital input signal trains without departing fromthe invention, it will be assumed hereinafter that the computer receivesits input information in the form of three difunction input signaltrains EX, EY, EH which are produced by converter 14 in response to theanalog i signals EX, EY and EH, respectively.

One form of structure which is available for converting an appliedanalog signal to a corresponding difunction signal train is disclosed inco-pending U.S. patent application Serial No. 540,699, filed October 17,1955, by Siegfried Hansen, for Analog-to-Difunction Converters, now U.S.Patent No. 2,885,662. Still another structure which represents animproved version of the foregoing device is disclosed in copending U.S.patent application Serial No. 592,963, filed June 21, 1956, forApparatus for Analog-to-Difunetion Conversion, by Daniel L. Curtis, nowU.S. Patent No. 2,885,663. In mechanizing converter 14, of course,either a single time-shared converter or three separate converters maybe employed for operating on the three input signals EX, EY and EH togenerate the three output difunction signals IDX, EY and QH,respectively. It should also be noted from FIG. 1 that converter 14 alsoreceives signals TPH, TPX and TPY` from computer 161; these signals, aswill be described in detail hereinbelow, are timing pulse signals eachof which divides time into what will hereinafter be termed difunctionsignal intervals, the timing signals being applied to converter 14 sothat each of the difunction signal trains x, lZiY and IDH issynchronized with the computer to present one difunction output signalduring each operational cycle of the computer as hereinafter described.

Before continuing with the general description of operation of theprojectile tracking computer of the invention, the manner in which inputintelligence is conveyed by a difunction signal should rst be discussedin more detail. It will be recalled that a difunction signal train maybe defined as a series of bivalued signals, each signal having either afirst value or a second value, the average of the signals in the trainrepresenting the average value of the quantity being conveyed. Thus, forexample, if the difunction signals represent either a plus or a minusone, the average value of the train over a given interval is obtained byadding the number of plus ones, subtracting the number of minus ones,and dividing the difference by the total number of signals occurringwithin the interval.

Consequently, a difunction train wherein the pattern +1, +1, +1, -1 iscyclically repetitive represents whereas a train wherein the callyrepetitive represents If now the analog signal EH representing height,for example, has a voltage range from -E to +E representing the heightrange from -20,000 feet to |20,000 feet, then a difunction pattern of+1, +1, +1, -1 represents +10,000 feet with respect to the radar, whilea difunction repetitive pattern of +1, 1, -l represents a -1/3 of therange in the negative direction, or +6,667 feet with respect to theradar.

Returning now to the description of FIG. 1, when the projectile trackingcomputer receives signal FR indicating that the radar is tracking aprojectile, and that consequently difunction signals 123x, EY and EH areavailable for sampling, appropriate gate circuits are opened within thecomputer to receive a predetermined number of difunction signals in eachof the input trains. More specifically, if it is assumed that theparticular embodiment of the invention here shown starts acceptingdifunction signals when the projectile is at point A1 in FIG. l, it Willaccept precisely 4096 difunction signals in each of the input trains, atthe end of which time the projectile is at a point A2 in its trajectory,and the computer will accept no further input information. With thisinformation the computer'is then operative, `as described hereinafter,to compute the coordinates X0, Y0 and Ho of the midpoint 7 M byaveraging the difunction on signals received, and to selectivelyextrapolate either forward or backward along the projectiles trajectoryto compute the coordinates of either the firing point FP or the impactpoint IP.

It should be noted that although the firing and impact points are shownin FIG. l to lie in plane XY, in practice the elevation of these pointswill depend upon the terrain; consequently, when the computerextrapolates forward or backward, the location of the impact and firingpoints is determined by referring to a topographical map of the area,the impact and firing points being given by the X, Y and H registerreadings when these readings coincide with a corresponding set of valuesdefining actual points on the associated map.

The X and Y registers preferably represent their respective coordinatesin meters owing to the fact that topographic maps customarily areplotted in meters. In particular, in the specific embodiment of theinvention to be shown and described each -j-l difunction signal indifunction trains X and DY preferably has a physical significauce of+21/2 meters and each -1 difunction a physical significance of -21/2meters. Consequently, the X and Y coordinates have a range of i4096 2V2or i10,240 meters, the X coordinate for example, having a value of10,240 meters if all 4096 difunction signals received are at their lowlevel, and a value of +10,240 meters if all 4096 difunction signals areat their high levels.

In a similar manner, the individual difunction signals in heightdifunction train EH are preferably scaled to have a significance of -}5feet or -5 feet, depending upon whether the signal is high or low,respectively. Thus the maximum height capable of being represented bydifunction input train EH is 4096 5 or 20,480 feet, the use of feetbeing preferred because topographical maps show elevation in feet.

Before setting forth in greater detail the structure and detailedoperation of the invention, consideration will be given to themathematical concepts involved in the operation of the computer and theequations which are mechanized therein.

MATHEMATICAL ANALYSIS velocity H. Thus the height coordinate may bewritten The vertical velocity term H may be expressed as the sum of theprojectiles vertical velocity VH at the known point and the sum of theincremental changes in velocity during the previously mentionedinterval, this latter term being the integral with` respect to time ofthe vertical acceleration H. Consequently, the vertical velocity may bewritten as:

H=VH+jiidf (2) The vertical accelerating forces operating on theprojectile in space are the acceleration of gravity g, and atmosphericdrag. While gravity is independent of velocity, drag is a function ofvelocity and may be expressed, within the projectile speeds of interest,as the product of a constant KH and the velocity. Thus the verticalacceleration of the projectile may be expressed as:

=tg+1 nf1i 3) Substituting Equation 3 in Equation 2 then gives:

H=vaftgdf+KHHdo 4) a Y In a similar manner, the X and Y coordinates ofthe projectile at any instant may be found from the equations:

X=X0+firdr (5) and where X0 and Y0 are the coordinates of a known pointon the trajectory of the projectile and X and Y represent the velocityvectors of the projectile along the X and Y coordinate axis.

Although the velocity vectors X and Y are of course independent ofgravity, they are effected by atmospheric drag. Accordingly the velocityvectors may be expressed x: VX-fKXXdf (7) and i/:VY-jKYidf (s) where KXand KY again represent constant drag factors,

and VX and VY are the velocities at the known point on the trajectory.

Referring once more to FIG. 1, it will be recalled that the computer ofthe invention is operative to compute the `average values of thedifunction signals transmitted to the computer during the interval inwhich the projectile moves from point A1 to point A2, and that theseaverage values when multiplied times the full scale range correspond tothe coordinates X0, Y0 and H0 of the midpoint M of the trackinginterval. In addition, as will be described hereinbelow with respect toFIG. 2, the intelligence information conveyed to the computer throughthe difunction signal trains may be utilized to determine the velocitiesVX, VY and VH of the projectile at the midpoint M. It will berecognized, therefore, that since the acceleration of gravity g and thedrag factors are constants, the computer of the invention has all of theinformation necessary to extrapolate Equations l, 5 and 6 backward tofind the coordinates of firing point FP, or to extrapolate the equationsforward to determine the coordinates of impact point IP.

Consider new the manner in which the difunction signals transmitted tothe computer during the tracking interval A1 to A2 may be employed forcomputing the velocities VH, VX and VY of midpoint M. With reference nowto FIG. 2, there is shown a plot of the trajectory in the plane of thetrajectory for illustrating the manner in which the height coordinate H0of the midpoint M is produced, and the manner in which the vertical orheight velocity VH is determined.

It will be noted first that the trajectory does not have a uniformslope, but instead follows a roughly parabolic curve at it moves frompoint A1 to point A2 through the interval T during which time, asaforesaid, the computer receives 4096 difunction signals in the train15H. Recall now that the average value of a difunction signal trainmultiplied by the full scale range corresponds to the average value ofthe variable position which the train represents. Accordingly, it willbe recognized that the height represented by the average of the train isthat of the point ldesignated HAVE in FIG. 2, and not the actual heightof the midpoint M above the XY plane of the radar. It may be shown,however, that the difference between the computer height HAVE and theactual height of midpoint M is ATZ as indicated in the drawing, where Ais equal to one-half the acceleration of gravity, or approximately 16feet per second, and T equals the duration of the tracking interval.

ggg, gnupg!! is a constant, it follows, thereis also a constant whichrepresents a constant error in height of the computed midpoint, theheight error being, for example, approximately 80 feet for a computerembodiment each of whose 4096 iterations is precisely 2 milliseconds induration.

It should be pointed out at this time that a correction for this errorin height is made when the computer is first set up for operation at aparticular point, and that the error is thenceforth completelycompensated. More specically, when the X, Y and H registers shown in thecomputer of FIG. 1 are adjusted to the yradar coordinates during systemset up, the H register is set to a value corresponding to the actualheight of the radar above sea level, plus eighty feet. Thereafter, itfollows from the above description, the height coordinate H of point Mcan be obtained by merely averaging input difunction train MH betweenthe times t1 and t5 in FIG. 2, the function being expressable by thefollowing equation:

t5 is Max rangeXZlH 20,480Z1ZlH t,

n it HO- T 4096 523MB feet (9) Continuing now with the description ofFIG. 2, the vertical velocity component VH is obtained by determiningthe first difference between the average height of the projectile duringthe interval t1 to t3 and the interval t3 to t5. More particularly, the4096 difunction signals generated in the interval T may be separatedinto two groups of signals each including 2048 difunction signals, thefirst group representing the average height of the projectile betweentimes l1 and t3, and the second group representing the average height ofthe projectile in the interval between points z3 and t5.

Again, as in the valuation of the height of midpoint M hereinabove, theaverage values represented by the two groups of difunction signals donot represent the true altitudes of midpoints P1 and P2 in the twosignal intervals, but are smaller than'the true altitudes by the errorsignal e which may be shown to be equal to V HAT AT t5 #a MaX rangeXZEH-l-e] rangeXZlZH-l-e] t3 t2 AT AT tu AT feet per difunction intervall 1) This last equation Will be recognized as stating that the B etvertical velocity VH at the midpoint M may be obtained by summing thetirst 2048 difunction signals in difunction train lZlH, subtracting theresult from the sum of the second group of 2048 difunction signals intrain DH, and dividing the diierence by the incremental time AT which inturn represents 2048 difunction signal intervals.

Through a similar analysis, the position coordinates X0 and Y0 ofmidpoint M, and the associated midpoint velocities VX and VY may beshown to be derivable by operating upon the input difunction signaltrains EX and lZly in accordance with the following equations:

t5 l5 Max rangeZ MX 10,2402JZ5X t1 ti is f5 VX: AT

meters per difunetion interval A T meters per dif unetion interval Itshould be noted that the derivation of these equations is simplilied bythe fact that there is no gravity force to be considered. It also willbe recognized by those familiar with digital computational techniquesthat Equations 9 through 15 indicate that the initial conditionsVrequired to solve Equations 1 and 4 through 8 may be derived by simpleaccumulation processes performed upon the difunction signal trainsreceived by the projectile tracking computer of the invention during thetracking operation.

:Consideration Will now be given to the general manner in which thecomputer operates, including the technique utilized for deriving therequisite initial conditions from the difunction signal trains, and thegeneral manner in which the computer then functions to solve thetrajectory equations.

GENERAL DESCRPTON OF COMPUTER OPERATION Table I Routine Function ClearSet-up subroutine..

Clear computer in preparation for computation. Set X, Y and H registersto radar coordinates. Derive from difunction signal trains the initialclzgnditions expressed in Equations 9 through Extrap o1 ate ForwardSolve trajectory equations for impact point. BackwardA Solve trajectoryequations for tiring point. Prepares computer for Fit Routine on thenext tracking operation.

The general operation of the computer in carrying out the foregoingroutines will be described with reference to FIG. 3 which is a blockdiagram of the computer.

Referring now to FIG. 3, the computer includes three computing sections300, 302 and 304 which are ern` ployed in conjunction with threerespectively associated digital servos 306, 308 and 310 for performingthe computational functions of the computer during the Fit andExtrapolate routines, the entry of the difunction signal trains 15H, IDXand EY during the Fit routine being controlled by a combined timing andgating circuit 312. As shown in FIG. 3, timing and gating circuit 312includes a timing signal generator 314 which generates the standardtiming pulse signal Tp referred to previously hereinabove, each signalmarking olf one difunction signal interval at the input converters.

The timing and gating circuit also includes a pair of counters 316 and318 which are actuable by start pulse FR received from the radar torespectively count off 4096 difunction signal intervals and 2048difunction signal intervals. In operation, counter 316 is used togenerate a signal representing the duration of the Fit subroutine, thissignal being utilized to control the transmission of precisely 4096difunction signals in the difunction trains 10H, 10X and lZlY to thecomputing sections 300, 302 and 304. The 2048 counter 318, on the otherhand, is utilized for separating the first group of 2048 difunctionsignals in each of the input trains from the second group, to therebyenable the derivation of the velocity vectors defined by Equations 1l,14 and 15.

In addition to the gating circuit 312 also includes an extrapolatecontrol circuit generally designated 332 which is employed to initiatethe extrapolate routine of the computer and to selectively signalextrapolation in either the forward direction to determine theprojectiles impact point, or in o the reverse or backward direction todetermine the projectiles firing point. As will be described below inmore detail, the direction of extrapolation is determined by controllingthe mathematical operations performed by the computing elements withincomputing sections 300, 302 and 304.

Referring once more to FIG. 3 each of digital servos 308 and 310 issimilar structurally to height servo 306, which will now be described indetail. Basically the servo is similar to the digital servo shown anddescribed in copending U.S. patent application Serial No. 525,148, ledon July 29, 1955 for Bidirectional Digital Rate Servo System, by thepresent inventor, now U.S. Patent No. 2,829,323. As shown in FIG. 3 theservo includes: a reversible motor 334 which is selectively energizablefrom a source 336 of direct-current potential under the control of amotor relay circuit 338; a digital quantizer 340 which is operative inconjunction with a pair of pick-off heads 342 and 34.4 for generating anoutput signal train which indicates incremental rotational movements ofa toothed disc 346 attached to the shaft of motor 334; an accumulatorregister 347 for receiving and accumulating the quantizer outputsignals; and feedback means, including a switch 348, a low pass lter 350and a buffer amplifier 352, for controlling the direction ofenergization of motor 334 in accordance with the value of the signalsstored in register 347.

In addition to the foregoing elements, the height servo 306 alsoincludes a mechanical shaft revolution counter 353 which presents avisual indication of the rotational position of the shaft of motor 334,a control switch 354 which is utilized for initially setting into themechanical counter the height coordinate of the radar, and a variableresistor 356 which is utilized for controlling the response of theservo. It should also be noted from FIG. 3 that the digital servo has analternate feedback circuit through switch 348 and a servo register 358which constitutes part of computing section 300 to be describedhereinafter, the output train from quantizer 340 being applied to theinput circuit of servo register 358 through an adder circuit 360.

Accumulator register 347 and servo register 358 are both basicallyelectronic digital accumulators, or more speciically, binary count-upcount-down counters, each foregoing elements, timing and a counterhaving a predetermined number of binary bit places and being responsiveto an applied train of bivalued signals for increasing the count storedtherein by one digit each time a signal representing one value isreceived, and for decreasing by one digit the count stored therein eachtime a signal of the opposite Value is received. In the operation of theservo, the most signicant digit of the binary number stored in one ofthe registers 347 and 358 is employed to control the energization ofmotor 334, servo register 358 being utilized when switch 348 is in itsnormal position, which represents the compute operation, whereasaccumulator 347 is utilized to control the motor energization whenswitch 348 is in its reset position.

Considering the operation of the accumulator and servo register withmore particularity, assume that in the null condition accumulator 347 isnormally cleared or in other words, contains all zeros, and that switch348 is in the reset position. Assume also that a Ibinary one in the mostsignificant digit, when presented as a low level signal and passed bytilter 350, energizes relay 338 to drive motor 334 in a clockwisedirection, while a binary zero in the most significant digit, whenpresented as a' high level signal and filtered, energizes relay 338 todrive the motor in the counter-clockwise direction. If then anincremental unit of clockwise or counter-clockwise rotation of the motorshaft causes the quantizer to put out either a -l or a +1 representingsignal, respectively, it will be seen that the servo register oscillatesback and forth between a binary number in which all digits are zeroesand a binary number in which all digits are ones. Accordingly,mechanical counter 353 will present a stabilized output display in whichthe least significant digit oscillates in amplitude in accordance withthe scaled significance of the quantizer output signals.

Assume now, however, that a relatively large binary number is placed inaccumulator 347, the only limitation imposed being that the mostsignificant digit of the number is zero if the number is positive or oneif the number is negative. When this is done the servo motor will beenergized to drive the mechanical counter in the appropriate directionuntil the quantizer feedback to the accumulator causes the number to bereduced so that the most significant digit changes from zero to plusone, or vice versa. Thereafter the servo register will oscillate for ashort period and finally stabilize in its null condition as describedhereinafter. It should be noted here that variable resistor 356 in themotor supply voltage permits the servo motor to operate at fullenergizing torque until the null point is passed, after which it enablesrapid damping of any oscillations which might occur.

At the conclusion -of the servo operation, therefore, the countpresented by the mechanical counter has been changed by the magnitude ofthe binary number which was stored in the servo register and in a sensecorresponding to the sign of the number; accordingly the mechanicalcounter has been servoed digitally in accordance with the binary numberwhich was entered in the accumulator. The manner in which the servooperates in conjunction with the remainder of the computer will bedescribed hereinbelow after a brief discussion of the structure ofcomputing sections 300, 302 and 304.

Referring once more to FIG. 3, computing sections 300, 302 and 304 areshown to include program sequencing gating networks 362, 363 and 364,respectively, and a plurality of digital integrators which areinterconnected therewith. Although the gating networks are shown in FIG.3 as three separate entities, it should be pointed out that in thedetailed embodiment of the invention to be described hereinafter asingle gating network is timeshared by all three computing sections.

With reference now to computing section 300 in particular, thecomputational processes are performed by servo register 358 and threedigital integrators 365, 366 and 367, respectively. Register 358, whichwill herein- 13 after be termed the H servo register, is utilized tocontrol the operation of the associated height servo 366 as previouslydescribed.

With respect to the structure of digital integrators 365, 366 and 367, acomplete and rigorous discussion of their basic functioning, from bothelectronic and mathematical standpoints, is set forth in detail incopending U.S. patent applications, Serial No. 388,780, filed October28, 1953, for Electronic Digital Differential Analyzer, and Serial No.564,683, filed February 10, 1956, for Electronic Digital DierentialAnalyzer, both by the `same inventor. As illustrated by integrator 365,a digital integrator comprises two registers termed the integrandregister and overflow register, here designated 368 and 370, which areoperative to store digital information in the form of signalsrepresenting binary t numbers, and a transfer network interconnectingthe two registers. In addition the integrator includes an output circuitfor presenting a train of bivalued signals representing the integralgenerated, a-nd a pair of input circuits one of which is coupled toregister 368 for receiving a train of bivalued signals representing theintegrand or the quantity to be operated upon, while the other inputcircuit is employed for applying to the transfer network a train ofbivalued signals representing the operand.

In operation, integra-nd register 368 is operable as an accumulator forsumming the signals in the applied signal train, while register 370 isutilized as an overflow register into which the binary number inregister 368 is cyclically either added or subtracted once each signalinterval, the particular operation performed depending upon the value ofthe operand signal received during the interval. The overllow digitsresulting from each of the additive transfers to the upper register 370are then eX- tracted during successive intervals to produce the outputtrain representative of the integral.

To more succinctly point out the operation of an integrator, considerthe application to register 368 of a difunction integrand signal [IHrepresenting the time rate of change of velocity, and the application tothe transfer network of an operand signal di representing time. It isapparent that register 368, operating as an accumulator, will produce abinary number representing the vertical velocity FI by summing thesignals in the train dH. It may be shown, then, that the output traingenerated by the integrator represents the function Illdt, as indicatedin the drawing.

It should be noted from FIG. 3 that integrators 366 and 367 in computingsection 300 do not include input circuits for receiving an integrandsignal train, but instead have constants stored in their lowerregisters, the height drag factor KH being stored in integrator 366whereas integrator 367 stores the acceleration constant g. Thus thesetwo integrators operate in essence as constant multipliers, their outputsignal trains representing the product-s of the operand times theconstants stored in their lower registers. It should be noted, however,that the projectile tracking computer of the invention operates in realtime, and that the operand signal dt applied to integrator 367represents either a -l-l or 1, depending upon whether the computer isextrapolating forward in time or backward in time.

Consider now the operation of the computer in carrying out in sequencethe routines set forth in Table I above. The computer Clear routine iscarried out when the radar is first set up at the desired mapcoordinates, and is utilized to clear accumulator 347, servo'register358, the upper and lower registers in integrator 365, and the upperregister in integrators 366 and 367 so that their contents representzero, the mechanism for accomplishing this routine not being shown inFIG. 3. It will be appreciated of course tha-t a similar routine iscarried out simultaneously in computing sections 362 and 304. It shouldalso be noted that those integrator registers carry- 14 ing constants,such as the lower registers in integrators 365 and 367, remainunaffected by the Clear routine.

In addition to clearing the computer, the Clear routine also permits aset-up subroutine to be carried out to enter into the mechanicalcounters the coordinates of the radar. More specilically, during theClear routine switch 354 is switched from its servo position, as shownin FIG. 3, to either the Up or Down position, to thereby energize motor334 to rotate counter 353 to present the corresponding map coordinate ofthe radar. This operation is carried out for each of the threecoordinates, it being remembered that the height visually displayed bythe H counter should be set to a quantity equal to the true altitude ofthe radar plus the previously discussed constant of feet. It should alsobe noted tha-t variable resistor 356 may be utilized to control themotor speed, and that while the set-up subroutine is being carried out,energy is removed from the motor relay 338 in each of the digitalservos.

After the Clear routine has been completed, the servo register in eachof the computer sections is coupled to its associated digital servo anda start signal is awaited from the associated radar indicating that atracking operation has commenced and to initiate the Fit routine. Inthis routine, the receipt of the Start signal FR, as shown in FIG. 3,opens a gate 372 in timing and gating circuit 312 to initiate thecounting operations within counters 316 and 318, counter 316 in turnfunctioning to open a gate 374 in program sequencing circuit 362 tothereby pass to servo register 358 the next 4096 difunction signals ininput train IDH.

During the period of the first 2048 difunction intervals in the samplinginterval, 4096 counter 316 functions to open a gate 376 in the programsequencing circuit to thereby accumulate the irst group of 2048difunction signals in register 368 of integrator 365 to present a numberrepresenting the average position of the projectile during the iirsthalf of the counting interval. At thel conclusion of this period 2G48counter 318 functions to close gate 376 and to open an inverting gate378 to thereby apply to register 368 the second group of 2048 signals inthe difunction train IDH, these signals being inverted or complemented.In this manner, the linal number standing in H register 368 representsthe summation of the iirst 2048 signals minus the summation of thesecond group of 2048 signals. In other words, the final number in theregister represents a solution to Equation 1l and is the value of thevertical velocity VH of the midpoint of the projectiles sampledtrajectory.

It should be apparent that the number standing in servo register 358, ifdigital servo 306 was not permitted to operate, would represent theheight coordinate H0 of the projectile at the midpoint in its sampledtrajectory, or in other words a solution to Equation 9. As a practicalmatter, however, as soon as servo register 358 starts to accumulatesignals in the difunction input signal train, digital servo 306 isunbalanced and motor 338 starts -driving counter 353 in a restoringdirection, the output signals from quantizer 340 being applied to adder360, along with the signals from gate 374, so that the servo registermaintains accurate position follow-up of counter 353.

At the conclusion of the Fit routine, gates 378 and 376 in programsequencing current 362 are `both closed and, consequently, no furtherdifunctio-n input signals are accepted. It should -be pointed out thatas a rule digital servo 306 will not yet have reached its nullpositions, and will therefore continue to drive mechanical counter 353in a restoring direction. It should be recognized however, that if theservo is permitted to drive to its null position, then the countvisually displayed by counter 353 will represent the altitude of themidpoint M in FIG. 2. A-fter the operator of the computer has received asignal indicating that the Fit routine has been terminated, he

may energize extrapolation circuit 332 to cause the computing sectionsto extrapolate the trajectory equations either backward to evaluate thering point or forward to evaluate the impact point.

`Consider now the manner in which the various integrators areinterconnected to solve the trajectory equations. It should be noted rstthat if the trajectory equaions are to lbe extrapolated forward intime,a signal dt representing a continuous train of plus one difunctionsignals is applied to the transfer networks of integrators 355 and 367so that the contents of the associated lower register are added to thecontents of the upper register once per iteration. Conversely, if theequations are to be extrapolated backward, a signal dt representing acontinuous train of minus one difunction signals is applied to thetransfer networks of these integrators so that the contents of the lowerregister are subtracted from the contents of the upper register once percomputational iteration.

Turning then to the elements of computing section 3%, if it is assumedthat the number stored in H register 368 represents the verticalvelocity then the output train presented by integrator 365 representsthe quantity dt. if this output train is applied to the transfer networkof integrator 366 to control its additive transfers, it will berecognized that the output train from this integrator will be KHdt,since the constant drag factor KH is stored in the lower register. In asimilar manner, the output train from integrator 367 may be shown to begdt .since the gravity acceleration constant g is stored in its lowerregister. By combining the output trains from integrators 366 and 367 inan adding network 378, a resultant sum signal train is producedrepresentative of the quantity (KHIIdt-l-gdt) as indicated in thedrawing, or stated differently, is representative of the velocityderivative al as may be vertified by differentiating Equation 4 `setforth above.

The resultant sum train is then passed by gate 380, which is opened'during the extrapolate routine, to the register of integrator 365 whichaccumulates the signals in the train dl to modify the original velocityvector VH stored therein during the Fit routine. Accordingly it will berecognized that integrators 365, 366 and 367 provide an iterativesolution of trajectory Equation 4.

The output train Hdt from integrator 365 is `also applied to servoregister 358 through a gate 382, which is opened during the extrapolateroutine, and through adder 360. It will be appreciated that the quantityHdt corresponds to the height derivative dH, as may be verified bydifferentiating Equation 1, the servo register `functioning toaccumulate the difunction signals in the input train and to furtherenergize the digital servo system in accordance with the summation ofthe received signals.

Before completing the generalized description of operation of theprojectile tracking computer of the invention, it should rst be pointedout that during the Fit and Extrapolate routines identical processes arecarried out substantially simultaneously in X and Y computing sections302 and 304 and their associated digital servos. More specically, itwill be recalled that program sequencing circuit 362 of H computingsection 300 is actually a gating matrix which is time-shared withcomputing sections 302 and 304, the sequencing circuit first beingutilized to yperform a single iteration for vertical velocity andheight, then Jror X velocity and X coordinate, then for Y velocity and Ycoordinate, and then back to vertical velocity and height.

With respect to the computational elements employed in computingsections 392 and 394, each includes a servo register yand twointegrators which `function in the same manner as servo register 358 andintegrators 36S and 366 in computing section 3h0, the only distinctionbeing that computing `sections 362 and 3h41 have no equivalent tointegrator 3o7 in computing, section 399 since the acceleration ofgravity is not a' function of the X and Y coordinates of trajectory.r`he servo registers are designated 384 and 336, respectively, while theX coordinate velocity and acceleration integrators are designated 383and 390 and the Y coordinate velocity and acceleration integrators aredesignated 3% and 394;. Thus, in the Extrapolate routine the outputtrains from the acceleration integrators in the X and Y computingsections are merely reapplied to the integrand registers of theassociated velocity integrators to thereby solve Equations 7 and 8,respectively, while the output trains of the velocity integrators `areapplied to the associated servo registers in their associated computersection to provide a solution to differential Equations 5 and 6,respectively.

Continuing now with the description of the Extrapolate routine, allthree computing sections are operable in synchronism to selectivelyextrapolate either forward or backward by successive iterations.Although not disclosed in detail in FIG. 3, the specific embodiment ofthe invention to be shown and described in detail hereinbelow providescontrols for either continuous extrapolation in the desired direction,extrapolation in groups of ve iterations, or extrapolation by utilizingonly a single iteration at a time. Inasmuch as thedigital servos areoperative continuously throughout both the Fit and Extrapolate routines,the choice of the extrapolate control to be employed is determined byhow close the position coordinates visually displayed in the mechanicalcounters of the digital servos approach the coordinates of a point onthe associated terrain map.

For example, assume that the coordinates displayed on the counters atthe conclusion of the Fit routine are those of a point high in theprojectiles trajectory, and that it is desired to evaluate theprojectiles firing point. The cornputer is then placed in continuousextrapolation in the backward direction until the servo countersindicate that the map coordinates of a point on the terrain are beingapproached. The continuous extrapolation is then stopped to permit thedigit `servos to null, after which the livesrtep or single-stepextrapolation switches are selectively energized in the appropriatedirection until the coordinates presented in the mechanical counters areidentical with the map coordinates of a point on the terrain. Thesecoordinates then represent the firing point. By applying a similartechnique of extrapolation in the opposite direction, on the other hand,the impact point of the projectile may be ascertained.

Having obtained the desired information the computer must now be resetto prepare for a subsequent tracking operation on another projectile. Inorder to fully comprehend the manner in which the Reset routine isaccomplished, it should first be understood that throughout the completerunning of the Fit and Extrapolate routines, the signals generated bythe quantizer in each of the digital servos are applied not only to theassociated servo register of the computing section, but also to theassociated accumulator register within each of the digital servos.Consequently when the projectiles impact or firing point has beendetermined, accumulator register 347 in digital servo 306, for example,contains a number whose magnitude and sign are representative of: theamplitude and sense of the numerical change of the count in counter 353in going from the original coordinates of the radar to the coordinatesof the firing point or impact point.

In carrying out the Reset routine, the servo loop in the digital servois changed by switch 348 so that motor 333 is energized from accumulator347, thereby driving the digital servo to a null whereat the accumulatoris emptied and the height counter again presents a visual indication ofthe radar altitude. Meanwhile similar operations carried outconcomitantly in digital servos 398 and 3l() return to theirrespectively associated output registers t the coordinates of the radar.In addition, the Reset routine is also employed to again clear the servoregister and the integrators in each of the computing sections in thesame manner as described previously for the Clear outine. The computeris then ready to again perform the Fit routine vof its computationaloperations whenever the radar again signals that a projectile is beingtracked. It should be here pointed out that the diagrammatic view of theinvention as shown in FIG. 3 illustrates the basic mode of operation ofthe projectile tracking computer, but does not necessarily show eachelement of the computer in its optimum form. For example, althoughswitches are shown to be utilized for controlling the Reset operation,in practice the output of either the servo register or accumulator isselectively gated electronically to control the energization of theassociated servomotor. In a similar manner, each of the accumulators,servo registers and integrators, shown as separate physical entities inFIG. 3 may be carried as Words in a magnetic drum recirculating memory,as will be described in detail hereinbelow. Y

DETAILED DESCRIPTION OF OPERATION In order to fully comprehend theoperation of the specific embodiment of the invention described indetail hereinbelow, it is first essential to understand the operation ofthe quantizers in the individual digital servos, the type and nature ofthe signals produced thereby, and the intelligence information conveyedIby these signals. With reference then to FIG. 4, there is shown aschematic ,diagram of a quantizer which may be utilized in height servo306 for presenting output signals representative of changes in therotational position of toothed disk 346 as detected by the previouslydescribed pick-olf heads 342 rand 344. f v

`As shown in FIG. 4, the quantizer includes an oscillator 400 whichproduces a sine wave `output signal which in turn is applied through atransformer 402 to a pair of series L-C circuits, one circuit includinga capacitor 404 and the inductance of pick-off head 344 while the othercircuit comprises a similar capacitor 406 and the in-V ductance ofpick-off head 342. In addition, the quantizer includes a pair ofdetection circuits 468 and 410 respectively associated with pick-offheads 344 and 342, respectively, each Vdetection circuit in turnincluding a plurality of rectiliers and capacitors for producing a pairof complementary voltage level output signals representative of theposition of its associated pick-olf relative to the teeth on ltootheddisk 346.

Both of pick-oli heads 342 and 344 are fixed relative to each other andare positioned adjacent the' outer periphery of toothed disk 346, eachhead comprising a horseshoe shaped ferromagnetic core which presentsthrough its associated winding a variable inductance Whose magnitude isdependent upon whether a tooth of disk 346 is beneath the air gap in itscore. More specifically, the inductance presented by each head is at amaximum when a tooth of disk 346 is adjacent its air gap, and is at aminimum when the air gap in its core is the space between adjacentteeth.

The value of the capacitor in each L-C circuit is seletced to provide anL-C series circuit resonant at the frequency of the applied signal whenthe inductance is at its maximum value. Consequently, when a tooth isadjacent the gap in a pick-olf head a relatively large alternatingcurrent signal is presented across the head, whereas a rela-tively smallalternating current signal is presented across the head when theinductance of the head is at its minimum value.

As further illustrated in FIG. 4, each detection circuit is connectedacross its associated pick-oit head and includes two parallel paths towhich the signal appearing across the head is applied by a pair ofcoupling capacitors 412 and 414, respectively, the parallel paths indetection circuit 403 functioning to produce a pair of complementaryoutput signals AH and AYH representative of the relative position ofhead 344 with respect to the teeth of disk 346, while similar paths incircuit 414k function to produce a pair of complementary output signalsBH and BH representative of the relative position of head 342. Theleft-hand path, as viewed in FIG. 4, includes a reference diode 416having its anode connected to a -27 volt source, not shown, and itscathode connected to capacitor 412 and to the anode of a blocking diode417, the other end of this diode being connected, in turn, to thecathode of a clamping diode 418, to one end of a pull down resistor 419,and to one terminal of an output capacitor 420. The other terminal ofcapacitor 420 is grounded while the second end of resistor 419 and theanode of diode 418 are connected respectively to a source of B- and to asource of -12 volts, either of which source is here shown.

The right-hand path in the detection circuit, in a similar manner,includes a reference diode 422 having its cathode connected to a +15volt source, not shown, and its anode connected to capacitor 414 and tothe cathode of a blocking `diode 423. The anode of diode 423 is thencoupled to a B+ source, not shown, by a pull-up resistor 424, to theanode of a clamping diode 425 whose cathode is connected to ground, andto one terminal of an output capacitor 426 whose other terminal isgrounded.

t In the absence of an applied alternating current signal, the voltageacross capacitor 42@ is normally `l2 volts since the pull-down resistorrenders diode 418 conductive, whereas the voltage across capacitor 426is at ground potential owing to the fact that diode 425 is renderedconductive from the B+ source through resistor 424. It also folows,therefore, that the junction of diodes 416' and 427 is floating midwaybetween l2 volts and `27 volts owing to the fact that diodes 416 and 417are both backbiased, while the junction of diodes 422 and 423 isfloating midway between ground and +15 volts since these two diodes areback-biased.

With reference n-ow to FIGS. 5a and 5b, there are shown the waveformsappearing at various points in the detection circuit as toothed disk 346is rotated from its position as shown, relative to head 344, to aposition Where one of the teeth is adjacent the gap in head 344. Asshown rby the left-hand portion of the waveforms in FIGS. 5a and 5b,when the head is adjacent a space in the disk a relatively smallalternating current signal is applied to the junction of diodes 416 and417 and to the junction of diodes 422 and 423 as shown `by waveforms416a and 422a, the peak-to-peak amplitude of the signal 'being less thanl5 volts so that all four of these diodes remain back-biased.Accordingly, the output signals AH and AH across capacitors 423 and 426are at -12 volts and ground potential, respectively.

Assuming then that disk 346 rotates so that a tooth is adjacent pick-ofthead 344, a signal of relatively large Iamplitude is impressed acrossthe junctions of diodes 416 and 417 and of diodes 422 and 423 asillustrated Iby waveforms 416g and 422:1, the signal causing diode 417to conduct as the signal raises the junction of diodes 416 and 417 abovel2 volts and causing diode 423 to conduct when its negative goingportion falls below ground potential. Consequently diodes 418 and 425become backbiased, and the voltage across capacitors 420 and 426 tendsto follow the signals passed by diodes 417 and 423.

As shown by the waveforms AH and AH, respectively, when the signalthereafter goes through regions of negative slope and positive slope,respectively, the voltage across capacitors 420 and 426 does not followthe waveforms 416a and 422g, but instead provides a form of envelopedetection analogous to the detection of the modulating signal in anamplitude modulated carrier signal. This result is produced by the factthat diodes 418 and 42S remain back-biased while the input signal islarge, and that diodes 417 and 423 are frontebiased `only when charge isbeing added to the capacitors and are back-biased as soon as thealternating current signal goes below the voltage on the associatedoutput capacitor. Consequently capacitors 420 and 426 have only a highimpedance discharge path during those portions of the input signal cycle'when they are not being charged from the input signal.

The structure and function of detection circuit 410 are identical to thestructure and function of circuit 408 described hereinabove, circuit 410-being operable to produce a pair of complementary output signals BH andBH representative of the position of pick-olf head 342 relative to disk346. For purposes of discussion hereinbelow, a high level or groundpotential in signal AH or BH will be termed a one-representing signal,while a -12 volt or low level voltage will be termed a zero-representingsignal. Conversely, complementary signals AH and B'H present aone-representing signal as a low level voltage and a zero-representingsignal as a high level voltage.

Consider next then the manner in which the quantizer, including its twodetection circuits, indicates a change in the rotational position oftoothed disk 346. With reference once more to FIG. 4, if each tooth ondisk 346 and an adjacent space are considered to be one cycle or oneincrement of rotation, then pick-off heads 342 and 344 are 90 out ofphase with respect to each other. Referring then to FIGS. 6a and 6b,there are shown the waveforms of signals AH and BH as they appear whendisk 346 is rotated at a constant speed, the waveforms of FIG. 6arepresenting clockwise rotation of disk 346 while the waveforms of FIG.6b represent counterclockwise r0- tation `of the disk. It will be seenthat waveform BH leads waveform AH by 90 when the disk is rotating in aclockwise direction, and lags waveform AH by 90 when the disk isrotating in a counterclockwise direction.

Assume now that one complete revolution of disk 346 actuates themechanical counter to produce a change of 100 feet in the altitudevisually displayed in the counter. Assume also that the maximum 4rate ofrotation of the toothed disk is one-twentieth of a revolution perdifunction interval, or in other words, is of l8 per iteration of thecomputer. It follows then that the maximum rate f change of the altitudepresented by the counter is 5 feet per difunction interval.

It will be apparent from the description set forth below, however, thatfor a five-toothed disk such as is utilized in the height servo, thequantizer is only capable of distinguishing between ten foot incrementsof altitude, inasmuch as the quantizer can respond only to such movementVof the disk as will produce a change in the output signals AH and BH,as previously described with regard to FIGS. 5a and 5b. Thus at the endof a difunction interval the quantizer output signals presented may beidentical to those presented at the end of the previous interval, andwill therefore indicate that no change has taken place in thecounter-reading. On the other hand, if the quantizer signals aredifferent from those presented at the end of the previous difunctioninterval, then a change of either plus ten feet or minus ten feet isindicated.

In the operation of the quantizer a change in the signal AH at the endof successive difunction intervals is utilized to indicate that thereading has changed by either plus ten feet or minus ten feet, whereasif the AH signal remains at the same level as before a zero change isindicated. The BH signal, on the other hand, is utilized to indicatewhether 4a change in altitude of ten feet is positive or negative, sinceas pointed out previously, the signal BH either leads or lags the signalAH 4depending upon whether the rotation of the counter is 4clockwise orcounterclockwise, respectively.

More specifically, it will be noted from FIG. 6a that the disk is-rotating in a clockwise direction if signal AH goes from itsone-representing value or high level to its zero-representing value orlow level and signal BH is at its zero-representing value or low level,whereas FIG. 6b

illustrates that a high level for signal BH when signal AH changes fromits high level to its low level indicates an increment of rotation inthecounterclockwise direction. In a similar manner these figures illustratethat a change in signal AH from its low level to its high levelrepresents an increment of clockwise rotation when signal BH is at itsIhigh level, and an increment of counterclockwise .rotation when signalBH is at its low voltage level. All of the foregoing conditions andtheir operation significance are correlated by the following table,Table II.

Table II Possible Prior Present Present Change in H conditions An An Bn0 0 0 0 No change. O 0 1 D0. 0 1 0 -10 feet. 0 1 1 +10 feet. 1 0 0 Do. 10 1 -10 feet. 1 1 0 0 No. change 1 1 1 D0.

It will be recognized from the foregoing table that it is necessary tostore signal AH at the end of each difunction signal interval so that itmay be compared with the signal AH as it is presented at the conclusionof the following interval to determine if there has been a change in itsvoltage level. As will be disclosed in more detail hereinbelow, thestorage of signal AH is accomplished in the detailed computer to behereinafter described by magnetizing a predetermined spot or cell in arecirculating magnetic memory in accordance with the level of thesignal.

The structure and operation of the quantizers in the X and Y digitalservos are substantially identical with that of the height servodescribed hereinabove, the only material distinction being that thesequantizers operate in conjunction with toothed disks which have tenteeth in lieu of five as in the height servo. More specifically, it willbe recalled that the difunction altitude or height is represented by adifunction train wherein each signal represents i5 feet, whereas theheight quantizer produces output signals representing either zero or 110feet, thereby setting up a 2:1 scale factor between the signals. Assumenow that one turn of the X and Y mechanical counters represents metersinstead of 100 feet, andthat the 2:1 scale factor between quantizeroutput signals and difunction input signals is to be maintained in orderto simplify the computers circuitry as described hereinafter. Inasmuchas each signal in the input difunction trains I/)X and EY has asignificance of 121/2 meters as discussed previously, it followstherefore that the quantizers in the X and Y servos must produce signalsrepresenting zero or i5 meters. Accordingly it will be recognized thatten teeth must be provided in the disks utilized in the X and Y servosto provide the 20 detectable transitions in rotational position whichare required to detect an incremental change of 5 meters in the rotationof a shaft where a complete revolution of the shaft signifies 100meters.

The manner in which the X and Y quantizers present their output signalsis identical with that previously discussed for the height servo, the Xquantizer generating output signals AX, AX, BX and B'X while the Yquantizer generates output signals AY, AY, BY and BY. Thus Table II, setforth hereinabove, is equally applicable to the X and Y quantizers withthe exception that changes in the X and Y coordinates presented by theassociated counters are represented by changes of t5 meters instead offeet.

With reference now to FIG. 7 there is shown in more detail thecomputational elements employed in a specific projectile trackingcomputer which has been constructed in accordance with the teachings ofthe-present invention. As shown in FIG. 7 the computer includes a frontpanel 700 on which are mounted the various computer controls and themechanical counters for displaying the results of the computation, arecirculating memory system including a magnetic drum unit generallydesignated 702 for storing applied electrical signals as magnetic cellson a magnetizable medium, a plurality of liip-ops or bistable storageelements which are designated by alphabetical characters, and a logicalgating matrix 704 which is operable under the control of the variousflip-flops for transferring intelligence information between the panelcontrols and magnetic drum unit 702, and for performing electrically thecomputational processes carried out within the computer.

In the particular embodiment of the invention shown in FIG. 7, magneticdrum unit 702 comprises a rotatable drum 706 having a magnetizableperiphery, a synchronous motor 708 energizable from a fixed frequencysource 710 for rotating the drum at a constant speed, and a plurality ofmagnetic transducers some of which are utilized for writing appliedelectrical signals as magnetized cells on the drum periphery and othersof which are employed for reading the magnetization of cells on the drumperiphery to present electrical output signals representative of themagnetization. The utilization of synchronous motor '708 and fixedfrequency source 7l0 is dictated by the fact that the computer mustperform its Fit routine in real time, and must therefore rotate drum 706through a predetermined angle during each difunction interval. It shouldbe noted, however, that it is not essential to employ a synchronousmotor, since au induction motor energized from a servo having precisionfollow-up may also be utilized to provide synchronous memory operation.

As indicated in FIG. 7 by the dotted lines on the periphery of drum 706,the drum surface is divided into tive channels or tracks designated C1,P1, P2, L1 and L2, each of which has one or more magnetic transducerspermanently associated therewith. More specifically, channel C1 is aclock or timing signal channel on which a predetermined number ofalternately polarized magnetic cells are permanently recorded, themagnetic pattern on this track being employed to energize an associatedreading transducer 7ll2 which in turn is coupled to a clock pulsegenerator 714 which produces a continuous train of high frequency pulsesfor synchronizing the operation of the computer through gating matrix704. In a similar manner channels P1 and P2 are also utilized to storepermanent predetermined patterns of magnetic cells; these two channelswill be termed the first and second marking channels and are operable inconjunction with a pair of respectively asociated reading transducers716 and 718 and a pair of reading amplifiers 719 and 720 for energizinga pair of channel reading flip-flops P1 and P2 in accordance with lthemagnetization of channels P1 and P2. Thus each of flip-flops P1 and P2presents at its output terminals a pair of complementary signal trainswhich are cyclically repetitive with each drum revolution and whosesequential signals correspond to the magnetization of the successivecells on their associated tracks. As will become more apparent from thedescription of FIG. 8 hereinbelow, channel P1 is utilized both alone andin conjunction with channel P2 to separate or distinguish diferentpieces of intelligence information stored in channels L1 and L2. ChannelP2, on the other hand, is also utilized to ystore signals representingthe constant acceleration factor g and the drag constants K11, KX and KYrequired to solve the trajectory equations previously described.

As shown in FIG. 7, channels L1 and L2 are different from thepermanently recorded channels described hereinabove in that they eachoperate in conjunction with a pair of magnetic transducers. Moreparticularly, chan-k nels L1 and L2 are recirculating registers utilizedto store serially the results of the computational processes carried outwithin the computer, and are operable in conjunction with a pair ofWriting transducers 721 and 722 and a pair of reading transducers '723and 724, respectively, the Writing transducers being energized from apair of Writing flip-flops M1 and M2 through a pair of respectivelyassociated writing amplifiers 725 and 726. The reading transducers, inturn, are employed to energize a pair of channel reading flip-flops L1and L2 through a respectively associated pair of reading amplifiers 727and 728.

ln the operation of the computer intelligence information is stored onthe surface of drum 706 in a serial fashion and in the form of binarybits, that is, as either a binary one or a binary zero. Stateddifferently, each track may be considered as an endless chain ofmagnetic cells each of which may be magnetized in one sense to representa binary one or in the opposite sense to represent a. binary zero, eachcell having a circumferential length about the drum equal to the lengthof each recorded clock pulse in channel C1. Accordingly, the readingamplifiers and their associated output flip-flops present a differentbinary information bit for each successive clock pulse interval, whilethe writing amplifiers and flip-flops M1 and M2 function to sequentiallyrecord in channels L1 and L2 a separate and distinct binary informationbit during each successive clock pulse interval.

Consider now the relative positions of writing transducers 721 and 722with respect to reading transducers 723 and 724. As Will be disclosed inmore detail hereinbelow, the computer performs one completecomputational iteration by operating on the H, X and Y coordinatesserially or in sequence during the interval required to present in readflip-flops L1 and L2 the binary bits previously stored'in iiip-liops M1and M2. Accordingly, the recirculating time of the L1 and L2 channels isprecisely one difunction time interval since it will be recalled thatduring the Fit routine one difunction input signal is received bythecomputer during each computational iteration.

Owing to the fact that permanent marking channels P1 and P2 arecontinuous around the drum while channels L1 and L2 are relatively shortrecirculating registers, it will also be recognized that the length ofthe drum periphery must be an integral multiple of the length of therecirculating registers so that the marks in the marking channels alwaysoccur concomitantly with predetermined intelligence bits in therecirculating registers. In the particular embodiment Vof the inventionhere shown and described, the periphery of drum 706 is precisely fivetimes the length of the recirculating registers; the reason for choosinga one to five ratio, as will be discussed more thoroughly hereinbelow,is to permit extrapolation of the :trajectory equations in groups oftive iterations at a time, or in other Words, to permit the computer toextrapolate through one entire drum revolution.

Consider now the rotational speed of drum 706 in a practical embodimentof the invention, and the number of clock pulses stored around the drum.It will be recalled from the description of FIGS. l and 2 that theduration of each difunction signal interval is 2 milliseconds;accordingly, one revolution of the drum then consumes ten milliseconds,since there are five difunction intervals per revolution. It follows,therefore, that the drum speed is 6,000 r.p.m., which may be obtainedfor example, by driving an eight pole synchronous motor from a 400 cycleper second source.

With respect to the number of clock pulses recorded around the drumperiphery, it will be apparent from the description of FIG. 8 set forthhereinafter that there are 133 bit spaces in each of the recirculatingchannels for spaans? performing the requisite computational functions.Consequently 4the drum has 5 l33==665 clock pulses recorded around itsperiphery. It should be noted here, incidentally, that the reading andwriting heads on the recirculating channels are separated by a distanceequal to the length of 131 magnetizable cells, rather than 133, owing tothe fact that read ilip-ilops L1 and L2 and write Hip-flops M1 and M2provide a memory for two of the binary bits in each of these channels.

With reference once more to FIG. 7, control panel 700 includes aplurality of switches for controlling the operation of the computer,some of these switches having been described previously with respect toFIG. 3. For example, switch 348 in FIG. 3 is also shown on control panel700 and is designated the routine control switch, this switch havingthree switching points designated Clear, Reset and Compute. When theswitch is set to the Clear position, a high level signal is presented tological gating matrix on the conductor designated C@ and a low levelsignal on conductor @E to indicat that the Clear routine is beingcarried out, while low and high level signals are presented onconductors and @3, respectively, to indicate that the Reset routine isnot being carried out. Conversely, when switch 348 is set to its Resetposition high level signals are presented on' conductors and (KV) andlow level signals on conductors( R' land@ to indicate that the Resetroutine is being carried out and not the Clear routine. On the otherhand when switch 348 is in its Compute position,

low level signal-s are presented on both the and@ conductors while highlevel signals are presented on conductors and Gi) to indicate thatneither the Clear nor Reset routine is being carried out. It should behere pointed out that when switch 348 is set to the Clear position, abiasing voltage is removed from certain ipflops in-the computer, asdescribed' in more detail hereinbelow, to force these Hip-Hops to theirzero-representing conduction states.

Continu-ing with the description of control panel 7%, when switch 348 isin its Compute position start signal FR `from 4the radar for initiatingthe Fit routine is passed on to a Fit control switch 730, this switchhaving three switch points designated Manual, Oft and Radar. When switch736 is in the Radar position the FR signal from the radar actuates arelay, not shown, which transmits Ia high level signal to theV logicalgating matrix over the conductor designated@ and a pulse signal over theconductor designated' (F-pulse); in addition the relay energizes thesignal lamp 732 indicating that the Fit routine is taking place. On theother hand, if switch 730 is in the 01T position, the radar start signalFR merely energizes lamp 732, the computer operator thereby beingnotified that he can manually initiate the Fit routine by switching tothe manual position, at which time a high level signal is presented overconductor It should be pointed out here that the conductor designated Eis complementary to conductor in that a high level signal is presentedon conductor E at all times except during the Fit routine when conductorpresents a high level signal.

As shown in FIG. 7 the control panel also includes the counter set-upswitch 354 previously described with respect to FIG. 3, and in additiona counter selector switch 734 which has three switch positionsdesignated H, X and Y and which is utilized in conjunction with switch354. More specifically, it will be recalled that in describing FIG. 3hereinabove, it was assumed for illustrative purposes that switch 354was associated with the height servo alone. In practice, however, asingle switch is utilized in conjunction with counter selector switch734 to selectively set-up the initial coordinates in each of H, X and Ycounters while the Clear routine is being carried out; thus whileroutine control switch 34S is in the Clear position, counter selectorswitch is moved sequentially to its H position, then to its X position,and tinally to its Y position, ineachof which positions switch 354 isselectively moved to-either its up position or down position to changethe coordinates visually presented by the correspondingly designatedmechanical counter.

It should be noted here that the computer also includes a single speedcontrol knob 736 which corresponds to the variable resistor designated356 in the height servo of FIG. 3, the speed control being utilized tocontrol the speed of all of the servomotors when switch 354 is in itsservo position, and being utilized to energize the single servo motordesignated by the setting of counter selector switch 734 during theclear routine when switch 354 is switched to its up or down position.

In addition to the foregoing control elements, panel 730 also includesthree diterent extrapolate control switches respectively designated 740,742 and 744 for providing either continuous extrapolation of thetrajectory equations after the conclusion of the Fit routine,extrapolation by tive iterations or steps, or extrapolation by a singleiteration or step. As shown in the drawing, each switch has a normalposition from which it can be moved to either the left or right toextrapolate the trajectory equations backward or forward, respectively.

Consider next the signals transmitted to logical gating matrix 704 bythe extrapolate control switches. When all three switches are in theirnormal positions, low level signals are transmitted to the matrix on theconductors designated (Back), (Forward), (1 cycle-down),

(5 cycle-down), and (continuous down), while high level signals aretransmitted to the matrix on the conductors designated l cycle-up), (5cycle-up), and (continuous up). Upon actuation of any of the threeswitches from its normal position, a high level signal is presented oneither conductor (Back) or the conductor (Forward), depending uponwhether the switch is moved to the left to extrapolate backwards or tothe right to extrapolate forward. In addition, the voltage statesnormally presented are reversed on the pair of conductors associatedwith the particular switch which has been actuated. For example, if thesingle-step switch 744 is moved to the left to extrapolate backwards byone iteration, high level signals are presented on conductors (Back) andon l cycle-down), whereas a low level signal is presented on conductor(1 cycle-up); the remaining conductors, on the other hand, remain attheir normal voltage levels. During the Extrapolation routine, ofcourse, conductor presents its aforementioned high level signal.

As indicated by the busses designated 746, 747 and 748 in FIG. 7, thethree quantizer output signals from each of the digital servospreviously described are also transmitted to logical gating matrix 764,while the matrix transmits three output signals OH, OX and OY back tothe control panel. These latter three sginals represent the outputsignals from the computer and are utilized to control the direction ofenergization of the servomotors in the digital servos during the Fit,Extrapolate and Reset routines. In terms of the digital servo structurepreviously described with respect to FIG. 3, signal OH is applied tofilter S in the height servo 306, while signals OX and OY are applied tosimilar filters in digital servos 3% and 31E), respectively.

Continuing now with the description of the basic elements of thespecific projectile tracking computer shown in FG. 7, the computer asshown includes nineteen ipops or bistable storage elements which areoperative in conjunction with memory unit 7t2, gating matrix 704, andthe input control switches to provide temporary storage for intelligenceinformation, to control the subcorrespondingly designated 25 lroutinescarried out within the computer, to control the mathematical operationscarried on within the computer, and to transfer intelligence informationto and from the memory unit.

Before describing the functions performed by the individual ilip-flops,consideration will be given lirst to the designation of the input andoutput conductors of the various flip-flops shown in FIG. 7. Eachflip-flop may comprise either vacuum tubes, transistors, magnetic cores,or any other elements suitable for providing bistable operation, andincludes a pair of input conductors which are designated the S inputconductor and Z input conductor, respectively, each conductor beingfurther designated by an alphabetical postscript corresponding to thealphabetical designation of its associated flip-flop. In addition, eachflip-flop includes a pair of output conductors one of which isdesignated by the same alphabetical ldesignation as the flip-flop fromvwhich it is taken, while the other is designated by the prime of thealphabetical designation of the flip-flop. Thus, for example, flip-HopK1 has both SK1 and ZKl input conductors and K1 and Kl outputconductors.

In operation each flip-flop will be assumed to he responsive to theapplication of an input signal to its S input conductor for setting to aconduction state corresponding to the binary value one, and to theapplication of an input signal to its Z input conductor for setting tothe opposite conduction state, which corresponds to the binary valuezero. In addition it will be assumed that when a flip-flop is in itsone-representing state the voltage presented on its correspondinglydesignated output conductor has a relatively high level value while thevoltage presented on its prime output conductor has a relatively lowlevel value. Conversely, when a flip-flop is in its zero-representingstate, the voltage presented on its output conductor has a low levelvalue whereas a high level voltage is presented on its prime outputconductor. For example, when flip-flop K1 is in its one-representingstate, high and low level signalsv are presented on output conductors K1and Kl, respectively, whereas these voltage levels are reversed whenflip-flop K1 is in its zero-representing conduction state.

Returning now to the description of FIG. 7, the flipops there shown maybe classified in six groups according to the functions they perform, twoof these groups having been discussed previously with regard to thedescription of memory unit 702. More specifically, flipops L1, L2, P1and P2 may be termed the memory reading group and function as electricalwindows for the correspondingly designated channels on drum 706 bysequentially presenting as output signal trains the magnetization ofsequential cells in the memory, each flip-flop assuming itsone-representing state when a binary one is read by its associatedreading transducer and its zerorepresenting state when a binary zero isread. Flip-flops M1 and M2, on the other hand constitute a memorywriting flip-flop group for recording information bits in channels L1and L2.

The remaining four groups of flip-flops are bracketed in FIG. 7 and aretermed counting group 750, program control group 752, temporary memorygroup 754, and computational group 756. The counting group designated750 comprises four flip-flops C1, C2, C3 and C4 which are operable as ascale-of-ten binary counter for distinguishing between or separating thevarious intelligence words stored in channels L1, L2, P1 and P2, as willbe illustrated more fully with respect to the description of FIG. 8hereinbelow. Program control group 752, on the other hand, includes twoflip-flops Q and R which function to provide signals to indicate whethera computational function is being carried out, and to preventreactuating the computer falsely when a computational func- 26 tion hasbeen carried out and the panel control switch which initiated thefunction has not yet been released.

The temporary memory flip-flop group including ipflops IH, IX and IY isutilized to store certain operational results produced during one passof the recirculating memories so that these results may be utilized inthe succeeding computational iteration. `More specifically, it will berecalled from FIG. 3 that during the extrapolate routine the outputsignal from integrator 365 is applied to integrator 366 to control itsadditive transfers, a similar operation being carried out in computingsections 302 and 304 as well. However, as will be shown in detail inFIG. 8, integrator 366 is operated upon in the serial recirculatingmemories before integrator 365 is operated upon; consequently flip-flopIH is utilized to store the output signal from integrator 365 until itcan be utilized for operating on integrator 366 during the subsequentmemory pass, while flip-flops IX and IY perform the identical functionfor the integrators in computing sections 302 and 304.

The functions performed by the computational flip-flop group 756 arerelatively complex and will be more clearly understood from the detaileddescription set forth hereinafter. Briefly, however, this flip-flopgroup includes flip-flops S1, K1, S2 and K2 which are operable inconjunction with read flip-Hops L1 and L2 and write flipflops M1 and M2for changing the magnitudes of the numbers stored in the variousintegrators and registers in accordance with the values of the inputreceived, for making additive transfers between the integratorregisters, and for controlling the operation of the 4096 counter and the2048 counter described hereinabove. i

Finally, it should be noted that the three timing pulse signals TPH, TPXand TPY utilized for interrogating the difunction converters describedin connection with FIG. l are transmitted to the associatedanalog-to-difunction converter from gating matrix 704, while the threeinput difunction signals from the converters are applied to the gatingmatrix. It will be noted that the three difunction trains are designatedIZVH, lx and lZ'Y in FIG. 7; the reavson for utilizing the complementarydifunction signals in this specific embodiment of the invention is thatit simpliiies the solution of the difference Equations l1, 14 and 15 aswill be described more fully below.

In order to comprehend more fully the detailed operation of theprojectile tracking computer of the invention, the arrangement ofintelligence information in the memory unit will now be described; itshould be noted that in computed parlance the sequence and arrangementof intelligence in the memory is termed the word structure, and isutilized frequently to teach the sequence of operation of the computer.

With reference now to FIG. 8, there is shown in graphic form the wordstructure of the computer as it appears at the reading flip-flops duringone difunction time interval, the sequence of appearance being fromright to left. As shown in FIG. 8, there are 133 clock pulses (Cp)presented during one pass of the recirculating register, the 133 digittime intervals dened by these clock pulses being divided into ten Wordsof varying length and designated g through Y. For purposes ofsimplicity, the g word will henceforth be termed the gravity word, whilethe words designated H, X, and Y will be termed the acceleration words.In a similar manner the words designated H, X and Y will be termed thevelocity words, whereas the words designated H, X and Y will be termedthe position words.

It will be noted from the word diagram that each of the position wordsincludes l5 binary information bits, each of the velocity words l2binary information bits, and each of the acceleration words, includingthe gravity Word, 13 binary information bits. The selection of thenumber of bits used to represent each word is made in View of theaccuracy required of the system, and the vnumber of iterations.

fact that the various integrators to be described hereinbelow mustbescaled with respect to each other to permit proper communication betweenintegrators and provide a resultant output signal scaled to actuate theservos described hereinabove.

With reference once more to FIG. 8 it Will be noted that marker channelP1 has a binary value of one recorded in the last digit place of eachword for demarking the end of each word, and a binary value of onerecorded in the rst digit place of each position word, the remainder ofthe digit places in the P1 marking channel having binary zeros recordedtherein. These marks, as wil'l be seen from the description below, areutilized to change the operations performed by the various iiip-ops incarrying out the computers computational processes, and for sequencingthe counting flip-flops -C1 through C4 in flip-flop group 750 in FIG. 7.In a similar manner, marker channel P2 also includes a binary one in thelast digit place of each Word, and in addition, has a binary value ofone recorded in the next to the last digit place of each velocity word.Ignoring for a moment the remaining digits stored in the accelerationwords of channel P2, it wil'l be noted that the next to last digit placein each of the velocity words has a binary one recorded therein whilethe next to last digit place in each of the position words has a binaryzero recorded therein.

Recall now that channels P1 and P2 extend around the entire memory drum,and are five time as long as the L1 and L2 recirculating channels, or inother words, the word structure of FIG. 8. In each of the P1 and P2channels, therefore, the recording pattern shown in FIG. 8 is repeatedprecisely live times so that the proper marks are presented in channelsP1 and P2 during each recirculation of channels L1 Vand L2. It will berecognized, however, that the computational processes carried out by thecornputer must be initiated at a predetermined instant in order Vfor theintelligence stored in the memory to be processed in the proper sequenceand for the specified The marker bit utilized for initiating thecomputational processes is termed the origin mark, and is represented bya binary value of one permanently recorded in the next to last digitplace of one of the ive Y position words which occur in a completerevolution of channel P2, the origin mark being indicated in FIG. 8 bythe dotted line 800. It will be recognized, therefore, 4that once duringeach complete revolution of the memory drum, flop-flop P2 will present aonerepresenting signal which corresponds to the origin mark andsignifies that the gravity word is about to be presented to be operatedupon.

Consider now the remaining binary bits stored in the acceleration wordsof channel P2. It will be remembered from the description of FIG. 7 thatthe constants g, K11, KX and KY are essential for extrapolating thetrajectory equations which are stored in the P2 channel. As shown inFIG. 8, the constant g is stored in the iirst twelve digit places of thegravity word sector of channel P2, While the constants KH, KX and KY arestored in the rst twelve digit places of the H, X and Y accelerationwords, respectively, of channel P2. It will be recognized, there-fore,that marker channel P2 serves as the integrand registers for integrators367, 366, 390 and 394 in FIG. 3. The values of the constants stored inthese registers and their representation will be discussed more fullybelow.

As pointed out hereinbefore, lthe markers at the end of the variouswords in the P1 and P2 channels are utilized in conjunction with counterflip-ops C1 through C4 to distinguish between the different words. Itwill also be recalled that these flip-Hops operate as a scale-of-te'ncounter for demarking the words, the output waveforms of hip-flops inperforming their counter function being shown in FIG. 8 by the waveformsC1, C2, C2 and C4. The conduction states of the flip-flops for thevarious words are correlated by the following truth table.

Table fIII 'Counter dip-dop states Yord -Ci C2 Ca C4 Y 1 o o 1 Y v0 l 01 It will be noted from this table that the Y coordinate words Y, Y andY are specified by the conduction states C'3C.1, the X coordinate wordsby the conduction states C2C4, the g word by C3C4, and the remainder ofthe H coordinate words 'by C3C.1. It will also be noted that within eachgroup of words associated with each coordinate, the acceleration Wordsare identified by conduction states C1C'2, the velocity words by theconduction state C1, and the position words by the conduction state C2.

Consider next the intelligence information stored in channels L1 and L2.As shown in FIG.8 the computer has a single 4096 counter whose count isstored in the gravity word of channel L1 to control the duration of theFit routine, and three 2048 counters whose counts are stored in theacceleration words of channel L1. It will be recalled that only a single2048 counter was shown in FIG. 3 for controlling the inputs to thevelocity registers. In practice, however, it has been found preferableto employ three separate 2048 counters located immediately preceding thethree velocity words for controlling the velocity word inputs during theFit routine, since it is then unnecessary to utilize an yadditional popfor holding throughout the three velocity words to indicate whether thefirst or second group of 2048 difunction input signals is beingreceived. It is clear, of course, that each of these threecountersoperate in an identical manner and store the same numericalcount.

Continuing with the description of FIG. 8, channel L2 is utilized as acomposite register channel which functions as the overow registers foral1 of the various integrators and also functions as the servoregisters. More specically, the gravity word sector of channel L2represents the overflow register of integrator 667 in FIG. 3,

while the acceleration words H, X `and Y represent the overow registersof integrators 366, 390 and 394 in FIG. 3. In a similar manner, theoverflow registers of velocity integrators 365, 388 and 392 in FIG. 3are represented by the velocity wordsII, X and Y in channel L2, whilethe position words H, X and Y function as servo registers 358, 384 and386, respectively. The remaining words in channel L1 are also utilizedin a manner analogous to the use of channel L2, the integrand registersof velocity integrators 365, 388 and 392 in FIG. 3 being represented bythe H, X and Y words of lchannel L1, while the H, X and Y Words of theL1 channel function as the accumulator registers in the digital servos306, 30S and 310, respectively.

Consider now the scaling of the various registers, or in other Words,the physical significance of a binary one stored in the various binarydigit spaces of the servo registers, accumulators, and the integratorregisters. It will be recalled lthat each +1 difunction signal in theinput difunction train IDH has a scaled significance of +5 feet and each-1 difunction signal has a scaled sig-

